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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 12675.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12675.p1 | 12675z1 | \([1, 0, 0, -7693, -270778]\) | \(-417267265/19773\) | \(-2386012358925\) | \([]\) | \(24192\) | \(1.1378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12675.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12675.p do not have complex multiplication.Modular form 12675.2.a.p
sage: E.q_eigenform(10)